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 Consider the line through the points $(1,2)$ and $(3,4)$.
 Determine a function $f$ whose graph is this line (be sure to write it in the form "$f\colon{\bf R}^n \to {\bf R}^m$ by $f(\ldots) = \ldots$").
 Determine a function $g$ whose image is this line.
 Determine a function $h$ whose level set is this line.
(Hint: the line will be the points that make your function equal to a specific constant. You may find that making the constant be $0$ is convenient.)
 In class, we saw how to represent a circle in the $xy$plane in three different ways (using three different functions, each using a different kind of set associated with that function).
Suppose you wanted to represent a sphere in space. What categories of function do you think you could use, and what set associated with each would you need to use? (You do not have to come up with formulas for this, just say what kind of $f\colon\R^n\to\R^m$ could be used, and which of the three sets you would need in each case.)

